An automatic transmission includes gear elements and clutches that may be used to execute a power downshift event. During a downshift, a transmission controller transfers torque from an offgoing clutch to an oncoming clutch to thereby shift the transmission to a lower gear. The controller ensures that a clutch associated with the current speed ratio in a clutch-to-clutch downshift, i.e., with the off-going clutch, releases while a clutch associated with a desired new speed ratio, i.e., with the on-coming clutch, smoothly engages. Turbine speed rises until the clutch speeds are synchronized, a value that is referred to as the sync speed. During the inertia phase of the downshift, the clutches slip and the speed ratio changes. The speed ratio does not change in the ensuing torque phase. Transmission output torque increases as the transmission shifts into the lower gear.